A 1-dimensional continuous and smooth model for thermally stratified storage tanks including mixing and buoyancy

被引:34
作者
Lago, Jesus [1 ,2 ]
De Ridder, Fjo [2 ]
Mazairac, Wiet [3 ]
De Schutter, Bart [1 ]
机构
[1] Delft Univ Technol, Delft Ctr Syst & Control, Mekelweg 2, Delft, Netherlands
[2] VITO, Energyville, Algorithms Modeling & Optimizat, ThorPk, Genk, Belgium
[3] ECOVAT, Poort Veghel 4946, Veghel, Netherlands
基金
欧盟地平线“2020”;
关键词
Thermal Storage; Stratified Tank; Modeling; Parameter Estimation; Optimal Control; Numerical Optimization; ENERGY-STORAGE; ELECTRICITY PRICES; OPTIMIZATION; POWER; PERFORMANCE; HEAT; FLEXIBILITY; INTEGRATION; SIMULATION; FRAMEWORK;
D O I
10.1016/j.apenergy.2019.04.139
中图分类号
TE [石油、天然气工业]; TK [能源与动力工程];
学科分类号
0807 ; 0820 ;
摘要
To mitigate the effects of the intermittent generation of renewable energy sources, reliable and efficient energy storage is critical. Since nearly 80% of households energy consumption is destined to water and space heating, thermal energy storage is particularly important. In this context, we propose and validate a new model for one of the most efficient heat storage systems: stratified thermal storage tanks. The novelty of the model is twofold: first, unlike the non-smooth models from the literature, it identifies the mixing and buoyancy dynamics using a smooth and continuous function. This smoothness property is critical to efficiently integrate thermal storage vessels in optimization and control problems. Second, unlike models from literature, it considers two types of buoyancy: slow, linked to naturally occurring buoyancy, and fast, associated with charging/discharging effects. As we show, this distinction is paramount to identify accurate models. To show the relevance of the model, we consider a real tank that can satisfy heat demands up to 100 kW. Using real data from this vessel, we validate the proposed model and show that the estimated parameters correctly identify the physical properties of the vessel. Then, we employ the model in a control problem where the vessel is operated to minimize the cost of providing a given heat demand and we compare the model performance against that of a non-smooth model from literature. We show that: (1) the smooth model obtains the best optimal solutions; (2) its computation costs are 100 times cheaper; (3) it is the best alternative for use in real-time model- based control strategies, e.g. model predictive control.
引用
收藏
页码:640 / 655
页数:16
相关论文
共 43 条
[1]   Assessment of a novel technology for a stratified hot water energy storage - The water snake [J].
Al-Habaibeh, Amin ;
Shakmak, Bubaker ;
Fanshawe, Simon .
APPLIED ENERGY, 2018, 222 :189-198
[2]   CasADi: a software framework for nonlinear optimization and optimal control [J].
Andersson, Joel A. E. ;
Gillis, Joris ;
Horn, Greg ;
Rawlings, James B. ;
Diehl, Moritz .
MATHEMATICAL PROGRAMMING COMPUTATION, 2019, 11 (01) :1-36
[3]   A validated model for mixing and buoyancy in stratified hot water storage tanks for use in building energy simulations [J].
Baeten, Brecht ;
Confrey, Thomas ;
Pecceu, Sebastien ;
Rogiers, Frederik ;
Helsen, Lieve .
APPLIED ENERGY, 2016, 172 :217-229
[4]   DYNAMIC PROGRAMMING [J].
BELLMAN, R .
SCIENCE, 1966, 153 (3731) :34-&
[5]  
Bergstra J, 2013, INT C MACHINE LEARNI, P115
[6]  
Bergstra J, 2011, ADV NEURAL INFORM PR, P2546, DOI 10.5555/2986459.2986743
[7]   Power-to-heat for renewable energy integration: A review of technologies, modeling approaches, and flexibility potentials [J].
Bloess, Andreas ;
Schill, Wolf-Peter ;
Zerrahn, Alexander .
APPLIED ENERGY, 2018, 212 :1611-1626
[8]  
Bock H. G., 1984, IFAC Proc., V17, P1603, DOI [DOI 10.1016/S1474-6670(17)61205-9, 10.1016/S1474-6670(17)61205-9]
[9]  
Boyd Stephen, 2004, Convex Optimization, DOI 10.1017/CBO9780511804441
[10]   Optimization of a residential district with special consideration on energy and water reliability [J].
Campana, Pietro Elia ;
Quan, Steven Jige ;
Robbio, Federico Ignacio ;
Lundblad, Anders ;
Zhang, Yang ;
Ma, Tao ;
Karlssona, Bjorn ;
Yan, Jinyue .
APPLIED ENERGY, 2017, 194 :751-764